A Practical Guide to Reliable Finite Element Modelling

Contents Chapter 1 Introduction and Overview 1.1 Purpose of the book 1.2 Finite Element Types - a Brief Overview 1.3 Finite Element Analysis and Finite Element Representations 1.4 Multi-Model Analyses 1.5 Consistency, Logic and Error Control. 1.6 Chapter Contents 1.7 References Chapter 2 Overview of Static Finite Element Analysis 2.1 Introduction 2.2 The Direct Method for Static Analyses 2.3 Reducing the Problem Size Chapter 3: Overview of Dynamic Analysis 3.1 Introduction 3.2 Element Mass Matrix 3.3 Additional Information that can be Extracted to Support a Dynamic Finite Element Analysis. 3.4 Forced Responses 3.5 Damped Forced Responses 3.6 Reducing the Problem Size Chapter 4: What's Energy Got to Do with It? 4.1 Introduction 4.2 Strain Energy 4.3 Potential Energy 4.4 Simple Bar 4.5 General Case 4.6 Minimum Potential Energy 4.7 The Principle of Minimum Potential Energy Applied to a Simple Finite Element Problem. 4.8 Finite Element Formulation 4.9 Direct Application to an Axial Bar Element 4.10 Convergence in Energy and Convergence in Stress 4.11 Results Interpretation 4.12 Kinetic Energy. 4.13 Final Remark Chapter 5 Preliminary Review of Errors and Error Control 5.1 Introduction 5.2 The Finite Element Process 5.3 Error and Uncertainty 5.4 Novelty, Complexity and Experience 5.5 Role of Testing 5.6 Initial Steps 5.7 Analysis Validation Plan (AVP) 5.8 Applied Common Sense 5.9 The Process Chapter 6 Discretisation: Elements and Meshes or Some Ways to Avoid Generated Error 6.1 Introduction 6.2 Element Delivery 6.3 Mesh Grading and Mesh Distortion 6.4 The Accuracy Ladder Chapter 7 Idealisation Error Types and Sources 7.1 Design Reduction and Idealisation Errors 7.2 Analysis Features 7.3 The Domain. 7.4 Levels of Abstraction 7.5 Boundary Conditions 7.6 Material Properties 7.7 Loads and Masses Chapter 8 Error Control 8.1 Introduction 8.2 Approach and Techniques 8.3 Accumulation of Errors and Uncertainties 8.4 The Role of Testing Chapter 9 Error Controlled Analyses 9.1 Introduction 9.2 Is the Finite Element System Fit for Purpose 9.3 Quality Report 9.4 The Error and Uncertainty Control Method Chapter 10 FEMEC Walkthrough Example 10 10.1 Introduction 10.2 FEMEC Static Analysis Illustrative Problem.